Optimization of headway, stops, and time points considering stochastic bus arrivals

With the capability to transport a large number of passengers, public transit acts as an important role in congestion reduction and energy conservation. However, the quality of transit service, in terms of accessibility and reliability, significantly affects model choices of transit users. Unreliable service will cause extra wait time to passengers because of headway irregularity at stops, as well as extra recovery time built into schedule and additional cost to operators because of ineffective utilization of allocated resources. This study aims to optimize service planning and improve reliability for a fixed bus route, yielding maximum operator’s profit. Three models are developed to deal with different systems. Model I focuses on a feeder transit route with many-to-one demand patterns, which serves to prove the concept that headway variance has a significant influence on the operator profit and optimal stop/headway configuration. It optimizes stop spacing and headway for maximum operator’s profit under the consideration of demand elasticity. With a discrete modelling approach, Model II optimizes actual stop locations and dispatching headway for a conventional transit route with many-to-many demand patterns. It is applied for maximizing operator profit and improving service reliability considering elasticity of demand with respect to travel time. In the second model, the headway variance is formulated to take into account the interrelationship of link travel time variation and demand fluctuation over space and time. Model III is developed to optimize the number and locations of time points with a headway-based vehicle controlling approach. It integrates a simulation model and an optimization model with two objectives - minimizing average user cost and minimizing average operator cost. With the optimal result generated by Model II, the final model further enhances system performance in terms of headway regularity. Three case studies are conducted to test the applicability of the developed models in a real world bus route, whose demand distribution is adjusted to fit the data needs for each model. It is found that ignoring the impact of headway variance in service planning optimization leads to poor decision making (i.e., not cost-effective). The results show that the optimized headway and stops effectively improve operator’s profit and elevate system level of service in terms of reduced headway coefficient of variation at stops. Moreover, the developed models are flexible for both planning of a new bus route and modifying an existing bus route for better performance

Optimizing feeder bus network based on access mode shifts

The methodology introduced in this dissertation is to optimally find a feeder bus network in a suburban area for an existing rail system that connects the suburban area with the Central Business District (CBD). The objective is to minimize the total cost, including user and supplier costs. Three major access modes (walk, feeder bus, and auto) for the rail station are considered and the cost for all modes makes up the user cost. The supplier cost comes from the operating cost of the feeder bus network. The decision variables include the structure of the feeder bus network, service frequencies, and bus stop locations. The developed methodology consists of four components, including a Preparation Procedure (PP), Initial Solution Generation Procedure (ISGP), Network Features Determination Procedure (NFDP) and Solution Search Procedure (SSP). PP is used to perform a preliminary processing on the input data set. An initial solution that will be used in SSP is found in ISGP. The NFDP is a module to determine the network related features such as service frequency, mode split, stop selections and locations. A logit-based Multinomial Logit-Proportional Model (MNL-PM) model is proposed to estimate the mode shares of walk, bus and auto. A metaheuristic Tabu Search (TS) method is developed to find the optimal solution for the methodology. In the computational experiments, an Exhaustive Search (ES) method is designed and tested to validate the effectiveness of the proposed methodology. The results of networks of different sizes are presented and sensitivity analyses are performed to investigate the impacts of various model parameters (e.g., fleet size, parking fee, bus fare, etc.)

Optimization Models for Improving Bus Transit Services

To provide efficient public transportation services in areas with high demand variability over time, it may be desirable to switch vehicles between different types of services such as conventional services (with fixed routes and schedules) for high demand periods and flexible route services during low demand periods. Thus, this dissertation analyzes and compares conventional, flexible, and variable type bus service alternatives. Optimization formulations and numerical results show how the demand variability over time and other factors affect the relative effectiveness of such services. A model for connecting one terminal and one local region is solved with analytic optimization. Then, models are extended to consider multiple regions as well as multiple periods. Numerical results of problems for multiple regions and multiple periods are also discussed. Secondly, a problem of integration of bus transit services (i.e., conventional and flexible services) with mixed fleets of buses is explored. A hybrid method combining a genetic algorithm and analytic optimization is used. Numerical analyses confirm that the total system cost can be reduced by integrating bus services with mixed fleets and switching service types and vehicles over time among regions in order to better fit actual demand densities. The solution optimality and the sensitivity of results to several important parameters are also explored. Thirdly, transit ridership may be sensitive to fares, travel times, waiting times, and access times. Thus, elastic demands are considered in the formulations to maximize the system welfare for conventional and flexible services. Numerical examples find that with the input parameters assumed here, conventional services produce greater system welfare (consumer surplus + producer surplus) than flexible services. Numerical analysis finds that conventional and flexible services produce quite acceptable trips with the zero subsidies, compared to various financially constrained (subsidized) cases. For both conventional and flexible services, it is also found that total actual trips increase as subsidies increase. When the cost is fully subsidized, conventional services produce 79.2% of potential trips and flexible services produce 81.9% of potential trips. Several methods are applied to find solutions for nonlinear mixed integer formulations. Their advantages and disadvantages are also discussed in the conclusions section

Optimizing integrated service for a transit route with heterogeneous demand

The methodology developed in this dissertation attempts to optimize integrated service that minimizes the total cost, including user and supplier costs, of a transit route with heterogeneous demand. While minimizing total cost, a set of practical constraints, such as capacity, operable fleet size and frequency conservation, are considered. The research problem is presented in three scenarios, consisting of various service patterns (e.g., all-stop, short-turn and express) under heterogeneous demand. A logit-based model was used to estimate passenger transfer demand. An exhaustive search method was developed to find the optimal solutions for a simplified transit route with six stops, and a Genetic Algorithm (GA) was developed to find the optimal solution for a real-world, large scale transit route. The optimized variables include the combination of service patterns, the associated service frequencies, and stops skipped by the express service. A six-stop transit route was designed and analyzed via a proof-of-concept demonstration to ensure that the developed models are capable of finding the optimal solutions. A sensitivity analysis was conducted, which enables transit planners to quantify the impact of various model parameters (e.g., user value of time, vehicle capacity, operating cost, etc.) to the decision variables and the objective function. Finally, the developed models and solution algorithm were applied to optimize integrated service for a real world bus route in New Jersey

The design of public transit networks with heuristic algorithms : case study Cape Town

Includes bibliographical references.The Transit Network Design Problem (TNDP) is well-researched in the field of transportation planning. It deals with the design of optimized public transportation networks and systems, and belongs to the class of non-linear optimization problems. In solving the problem, attempts are made to balance the tradeoffs between utility maximization and cost minimization given some resource constraints, within the context of a transportation network. In this dissertation, the design of a public transit network is undertaken and tested for Cape Town. The focus of the research is on obtaining an optimal network configuration that minimizes cost for both users and operators of the network. In doing so, heuristic solution algorithms are implemented in the design process, since they are known to generate better results for non-linear optimization problems than analytical ones. This algorithm which is named a Bus Route Network Design Algorithm (BRNDA) is based on genetic algorithms. Furthermore, it has three key components namely: 1) Bus Route Network Generation Algorithm (BRNGA) - which generates the potential network solutions; 2) Bus Route Network Analysis Procedure (BRNAP) - which evaluates the generated solutions; 3) Bus Route Network Search Algorithm (BRNSA) - which searches for an optimal or near optimal network option, among the feasible ones. The solution approach is tested first on a small scale network to demonstrate its numerical results, then it is applied to a large scale network, namely the Cape Town road network

Data-Driven Optimization Models for Feeder Bus Network Design

Urbanization is not a modern phenomenon. However, it is worthwhile to note that the world urban population growth curve has up till recently followed a quadratic-hyperbolic pattern (Korotayey and Khaltourina, 2006). As cities become larger and their population expand, large and growing metropolises have to face the enormous traffic demand. To alleviate the increasing traffic congestion, public transit has been considered as the ideal solution to such troubles and problems restricting urban development. The metro is a type of efficient, dependable and high-capacity public transport adapted in metropolises worldwide. At the same time, the residents from crowded cities migrated to the suburban since 1950s. Such sub-urbanization brings more decentralized travel demands and has challenged to the public transit system. Even the metro lines are extended from inner city to outer city, the commuters living in suburban still have difficulty to get to the rail station due to the limited transportation resources. It is becoming inevitable to develop the regional transit network such as feeder bus that picks up the passengers from various locations and transfer them to the metro stations or transportation hubs. The feeder bus will greatly improve the efficiency of metro stations whose service area in the suburban area is usually limited. Therefore, how to develop a well-integrated feeder system is becoming an important task to planners and engineers. Realizing the above critical issues, the dissertation focus on the feeder bus network design problem (FBNDP) and contributes to three main parts: 1. Develop a data-mining strategy to retrieve OD pair from the large scale of the cellphone data. The OD pairs are able to present the users’ daily behaver including the location of residence, workplace with the timestamp of each trip. The spatial distribution of urban rail transit user demand from the OD pair will help to support the establishment and optimization of the feeder bus network. The dissertation details the procedure of data acquisition and utilization. The machine leaning is applied to predict the travel demand in the future. 2. Present a mathematical model to design the appropriate service area and routing plans for a flexible feeder transit. The proposed model features in utilizing the real-world data input and simultaneously selecting bus stops and designing the route from those targeted stops to urban rail stops. 3. Propose an improved feeder bus network design model to provide precise service to the commuters. Considering the commuters are time-sensitive during the peak hours, the time-windows of each demand is taken in to account when generating the routes and the schedule of feeder bus system. The model aims to pick up the demand within the time-windows of the commuters’ departure time and drop off them within the reasonable time. The commuters will benefit from the shorter waiting time, shorter walking distance and efficient transfer timetable

Optimization Methods in Modern Transportation Systems

One of the greatest challenges in the public transportation network is the optimization of the passengers waiting time, where it is necessary to find a compromise between the satisfaction of the passengers and the requirements of the transport companies. This paper presents a detailed review of the available literature dealing with the problem of passenger transport in order to optimize the passenger waiting time at the station and to meet the requirements of companies (maximize profits or minimize cost). After a detailed discussion, the paper clarifies the most important objectives in solving a timetabling problem: the requirements and satisfaction of passengers, passenger waiting time and capacity of vehicles. At the end, the appropriate algorithms for solving the set of optimization models are presented

Optimizing fare structure and service frequency for an intercity transit system

This study presents an approach to jointly optimize service headway and differentiated fare for an intercity transit system with an objective of total profit maximization and with consideration given to the economic and social sustainability of the system. Service capacity and fleet size constraints are considered. The optimization problem is structured into four scenarios which are comprised of the combinations of whether the Ranges of Travel Distance (RTD) is fixed or variable and if the time period is for a single period or for multiple periods. A successive substitution method (specifically, a modified Gauss Southwell method) is applied to solve for the optimal solutions when the RTD is considered fixed, while a heuristic solution algorithm (specifically, a Genetic Algorithm) is developed to find the optimal solutions when the RTD is considered to be optimized. The methodology discussed in this dissertation contributes to the field of transportation network modeling because it establishes how to solve the fare and headway design problem for an intercity transit system. Intercity transit agencies are faced with the challenge of determining fares for a very complicated setting in which demand elasticity, realistic geographic conditions, and facility locations of the transit system all must be taken into account. A real world case study - Taiwan High Speed Rail is used to demonstrate the applicability of the developed methodology. Numerical results of optimal solutions and sensitivity analyses are presented for each scenario. The sensitivity analyses enable transit planners to quantify the impact of fare policies and address social equity issues, which can be a major hurdle of implementing optimal fare policy to achieve maximum profit operation. According to the sensitivity analysis, the total profit surfaces for various headways, fares, and RTD are relatively flat near the optimum. This indicates that the transit operator has flexibility in shifting the solution marginally away from the optimum without significantly reducing the maximum profit. By varying the elasticity parameters of fare and demand one can observe how these variables affect the optimized RTD. The results indicate that as the elasticity parameters of fare increase or demand decreases, the optimal number of RTD increase while the boundaries of RTD are concentrated in the range of shorter travel distances

A first approach to the optimization of Bogotá's TransMilenio BRT system

Bus rapid transit (BRT) systems are massive transport systems with medium/high capacity, high quality service and low infrastructure and operating costs. TransMilenio is Bogotá's most important mass transportation system and one of the biggest BRT systems in the world, although it only has completed its third construction phase out of a total of eight. In this paper we review the proposals in the literature to optimize BRT system operation, with a special emphasis on TransMilenio, and propose a mathematical model that adapts elements of the above proposals and incorporates novel elements accounting for the features of TransMilenio system